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Two trains, 200 km apart, are moving toward each other at the speed of 50 km/hour each. A fly takes off from one train flying straight toward the other at the speed of 75 km/hour. Having reached the other train, the fly bounces off it and flies back to the first train. The fly repeats the trip until the trains collide and the bug is squashed.

What distance has the fly traveled until its death?

(There is a complicated and an easy way to solve this math brain teaser.)

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

There is a complicated way counting a sequence. Or simply knowing that if the fly is flying the 2 hours still at the same speed of 75 km/h then it flies a distance of 150 km.

Two trains 200 km from each other are moving at the speed of 50 km/hour towards each other. From one train a fly takes off (Edit: at the moment the trains are 200 km from each other), flying straight (upon the rails) to the other train at the speed of 75 km/hour (Edit: 75km/hour relative to ground), bounces away from it and flies back to the first train. This is repeated till the trains crash into each other and the fly is smashed.

What distance is the fly able to fly until its death?

(There is a complicated and an easy way to solve this math brain teaser.)

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I just want to say that I am very proud of this specific question because it is the only one I've seen that doesn't have the same questions and the same wrong answers being repeated a hundred times. Wrong answers are fine. But if you read and find out that they were already proven wrong, then you wouldn't be posting it. And if you're going to post something, shouldn't you read the previous posts to make sure you're not repeating? That happens a lot and this is the first I've seen that it hasn't happened. I'ts made a nerd very happy.

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what u have to take into consideration is that when the fly hits the other train, it will die. it would have to slow down first. then when it goes back, it will have to speed back up, therefore causing less travel time/distance

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ok this might be a stupid question but how do you know it takes 2 hours? the puzzle never says so.

Two trains 200 km from each other are moving at the speed of 50 km/hour towards each other.

Each train is going 50 km/hour, they are traveling in opposite directions towards each other, and they are initially 200 km apart. The distance between the trains is decreasing at a rate equal to the sum of the speed of each train, or 100 km/hour.

It will take 2 hours to close the gap.

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I'd like to point out that there is a minor detail which has not been considered. Assuming that the fly begins his suicidal flight at the precise time that the trains are at their original points, then the calculation presented would be correct. However, the puzzle, as stated, does not in fact say when the fly begins his spiraling death. If he were to start flying half way through the trip for example, then he would only travel 75km. Therefore, unless the puzzle is reworded, the answer would rely on the point in which the fly has his nervous break down and decides that existence is futile.

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The easy way is to calculate the time when both the trains crashes which is 200/100=2hours (100km/h is the respective speed of the trains) now simply multiply the speed of fly to get distance traveled which is 75*2=150 km (Does this gives result........ )

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I'd like to point out that there is a minor detail which has not been considered. Assuming that the fly begins his suicidal flight at the precise time that the trains are at their original points, then the calculation presented would be correct. However, the puzzle, as stated, does not in fact say when the fly begins his spiraling death. If he were to start flying half way through the trip for example, then he would only travel 75km. Therefore, unless the puzzle is reworded, the answer would rely on the point in which the fly has his nervous break down and decides that existence is futile.

fast fly, and ...

oes it take off from the engine of the train or the caboos?

how long is the train that it leaves from?

i seen a lot of posts with questions like this today and i'm not sure if it's people over thinking the problem, or just trying to appear more intelligent that they are by asking questions that can be inferred. if the length of the train is not mentioned ... IT DOESN'T MATTER.

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the 2 trains will collide after 2 hrs, since both are travelling at a rate of 50kph... the distance they will travel will be 100kms. this will also be the same time the fly will travel. applying the formula distance travelled = speed multiplied by time, 75 km/hr x 2hrs, will gie a result of 150km...

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i seen a lot of posts with questions like this today and i'm not sure if it's people over thinking the problem, or just trying to appear more intelligent that they are by asking questions that can be inferred. if the length of the train is not mentioned ... IT DOESN'T MATTER.

Well, the question doesn't state that the trains are on the same track, so can we be SURE that they will even collide? Maybe the trains pass right by each other and the fly is free to keep flying between them as long as he can fly? Which makes for another interesting brain teaser/math problem...........would the fly be able to touch each train 3 times in 1 hour, after the trains pass each other????? Assume that the trains are still moving 50 kph and the fly is going 75 kph.

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I'd like to point out that there is a minor detail which has not been considered. Assuming that the fly begins his suicidal flight at the precise time that the trains are at their original points, then the calculation presented would be correct. However, the puzzle, as stated, does not in fact say when the fly begins his spiraling death. If he were to start flying half way through the trip for example, then he would only travel 75km. Therefore, unless the puzzle is reworded, the answer would rely on the point in which the fly has his nervous break down and decides that existence is futile.

I know these puzzles are old, but I just started getting them on my iGoogle page and this one just came up. My original question before trying to answer was when the fly took off from the first train. I give Kudos to Dreaken667 because of the terminology used of the fly beginning his suicidal flight ... bc of his nervous break down and deciding his existence is futile. We humans have a tendency to wish we were a fly on the wall of someone when something specific happens; but to try to imagine why a fly would make a suicide flight is just too much. So, it would have to be assumed in human logic that the fly had a nervous breakdown and felt his life could make no difference so why not fly to its death and have someone make a puzzle out of it! I thought it was worth a laugh:D

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I think this is a solid puzzle, if you want to make it a little more technically correct, it should say that the fly is flying at 75kph relative to ground. I only say this because as soon as i saw the words "the fly takes off from the train" I thought he was flying at 50kph from being on the train and you add that to the 75 (if it was relative to the train) for a total velocity of 125kph relative to ground. Its really probably not an issue for anyone other than me and most people would assume it, but it is more technical.

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I think this is a solid puzzle, if you want to make it a little more technically correct, it should say that the fly is flying at 75kph relative to ground. I only say this because as soon as i saw the words "the fly takes off from the train" I thought he was flying at 50kph from being on the train and you add that to the 75 (if it was relative to the train) for a total velocity of 125kph relative to ground. Its really probably not an issue for anyone other than me and most people would assume it, but it is more technical.

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Easy, if the fly is inside the train and flys in a relative direction equal to the direction of the train, the fly will be going faster than the train relative to the tracks.

As it applies in this question, i don't know. It's just a puzzle.

If this were in a vacuum you'd be right, but the air between the trains is actually moving at 0mph (presumably) so it still doesnt make sense that a fly can go 75 km/h. But this is a puzzle, and a very clever one at that, so I will stop with the annoying harshness of reality.

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"Two trains 200 km from each other are moving at the speed of 50 km/hour towards each other."

I have a problem here. By definition if they are moving at 50km/h towards each other then they are each moving an average of 25kph. I don't know why everyone seems to think that "50 km/h towards each other" means each train is moving at 50 kph towards the other train. If each train where moving an average of 50km/h then they would be moving at a rate of 100kmph towards each other.